Browsing by Author "Rehman, Muhammad Aziz-u"

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Novel numerical analysis for nonlinear advection-reaction-diffusion systems
(2020) Baleanu, Dumitru; Ahmed, Nauman; Baleanu, Dumitru; Alshomrani, Ali Saleh; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-u; Shaikh, Tahira Sumbal; Malik, Muhammad Rafiq; 56389
In this article, a numerical model for a Brusselator advection-reaction-diffusion (BARD) system by using an elegant numerical scheme is developed. The consistency and stability of the proposed scheme is demonstrated. Positivity preserving property of the proposed scheme is also verified. The designed scheme is compared with the two well-known existing classical schemes to validate the certain physical properties of the continuous system. A test problem is also furnished for simulations to support our claim. Prior to computations, the existence and uniqueness of solutions for more generic problems is investigated. In the underlying system, the nonlinearities depend not only on the desired solution but also on the advection term that reflects the pivotal importance of the study.
Structure preserving algorithms for mathematical model of auto-catalytic glycolysis chemical reaction and numerical simulations
(2020) Baleanu, Dumitru; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-u; Khan, Ilyas; Ali, Mubasher; Nisar, Kottakkaran Sooppy; 56389
This paper aims to develop positivity preserving splitting techniques for glycolysis reaction-diffusion chemical model. The positivity of state variables in the glycolysis model is an essential property that must be preserved for all choices of parameters. We propose two splitting methods that remain dynamically consistent with the continuous glycolysis reaction-diffusion model. The proposed methods converge to a true steady-state or fixed point under the given condition. On contrary to the classical operator splitting finite difference methods, we use nonstandard finite difference theory to propose a new class of operator splitting techniques.